Necessary and sufficient conditions for boundedness of commutators associated with Calderon-Zygmund operators on slice spaces

作者：Lu, Yuan; Zhou, Jiang^*; Wang, Songbai

来源：Annals of Functional Analysis, 2022, 13(4): 61.

DOI：10.1007/s43034-022-00209-1

• Calderon-Zygmund operator
• BMO(R-n)
• Lip(alpha)(R-n)
• Slice space

Let t is an element of (0, infinity) and r, p is an element of (1, infinity). In this paper, we establish new versions of the Fefferman-Stein inequality over the slice space (E-r(p))(t)(R-n), and further reobtain the boundedness of the Calderon-Zygmund operators with the standard kernel via a direct way rather than the extrapolation on slice spaces. Furthermore, we give two necessary and sufficient conditions for the boundedness of the commutator [b, T-Omega] generated by the locally integrable function b and the Calderon-Zygmund operator with the rough kernel T-Omega on slice spaces.

• 单位
  新疆大学